Chapter-3-1 Chemistry 481, Spring 2015 Instructor: Dr. Upali Siriwardane Office: CTH 311 Phone Chemistry 481(01) Winter 2015

Chapter-3-2 Chemistry 481, Spring 2015 Chapter 3. Structures of simple solids Crystalline solids: The atoms, molecules or ions pack together in an ordered arrangement Amorphous solids : No ordered structure to the particles of the solid. No well defined faces, angles or shapes Polymeric Solids: Mostly amorphous but some have local crystiallnity. Examples would include glass and rubber.

Chapter-3-3 Chemistry 481, Spring 2015 The Fundamental types of Crystals Metallic: metal cations held together by a sea of electrons Ionic: cations and anions held together by predominantly electrostatic attractions Network: atoms bonded together covalently throughout the solid (also known as covalent crystal or covalent network). Covalent or Molecular: collections of individual molecules; each lattice point in the crystal is a molecule

Chapter-3-4 Chemistry 481, Spring 2015 Metallic Structures Metallic Bonding in the Solid State: Metals the atoms have low electronegativities; therefore the electrons are delocalized over all the atoms. We can think of the structure of a metal as an arrangement of positive atom cores in a sea of electrons. For a more detailed picture see "Conductivity of Solids". Metallic: Metal cations held together by a sea of valence electrons

Chapter-3-5 Chemistry 481, Spring 2015 Metal Atom Packing Close packing Loose packing

Chapter-3-6 Chemistry 481, Spring 2015 Metal Atom Packing

Chapter-3-7 Chemistry 481, Spring 2015 Metal Atom Close Packing

Chapter-3-8 Chemistry 481, Spring 2015 Packing and Geometry Close packing ABC.ABC... cubic close-packed CCP gives face centered cubic or FCC(74.05% packed) gives face centered cubic or FCC(74.05% packed) AB.AB... or AC.AC... (these are equivalent). This is called hexagonal close-packing HCP CCP HCP

Chapter-3-9 Chemistry 481, Spring 2015 Loose packing Simple cube SC Body-centered cubic BCC Packing and GeometryPacking and Geometry

Chapter-3-10 Chemistry 481, Spring 2015 Unit Cell Dimensions The unit cell angles are defined as: , the angle formed by the b and c cell edges , the angle formed by the a and c cell edges , the angle formed by the a and b cell edges a,b,c is x,y,z in right handed cartesian coordinates a  b  c  a

Chapter-3-11 Chemistry 481, Spring 2015 Bravais Lattices & Seven Crystals Systems In the 1840’s Bravais showed that there are only fourteen different space lattices. Taking into account the geometrical properties of the basis there are 230 different repetitive patterns in which atomic elements can be arranged to form crystal structures.

Chapter-3-12 Chemistry 481, Spring 2015 Fourteen Bravias Unit Cells

Chapter-3-13 Chemistry 481, Spring 2015 Seven Crystal Systems

Chapter-3-14 Chemistry 481, Spring 2015 Number of Atoms in the Cubic Unit Cell Coner- 1/8 Edge- 1/4 Body- 1 Face-1/2 FCC = 4 ( 8 coners, 6 faces) SC = 1 (8 coners) BCC = 2 (8 coners, 1 body) Face-1/2 Coner- 1/8 Edge - 1/4 Body- 1

Chapter-3-15 Chemistry 481, Spring 2015 Close Pack Unit Cells CCP HCP FCC = 4 ( 8 coners, 6 faces )

Chapter-3-16 Chemistry 481, Spring 2015 Simple cube SC Body-centered cubic BCC Unit Cells from Loose PackingUnit Cells from Loose Packing SC = 1 (8 coners) BCC = 2 (8 coners, 1 body)

Chapter-3-17 Chemistry 481, Spring 2015 Coordination Number The number of nearest particles surrounding a particle in the crystal structure. Simple Cube: a particle in the crystal has a coordination number of 6 Body Centerd Cube: a particle in the crystal has a coordination number of 8 Hexagonal Close Pack &Cubic Close Pack: a particle in the crystal has a coordination number of 12

Chapter-3-18 Chemistry 481, Spring 2015 Holes in FCC Unit Cells Tetrahedral Hole (8 holes) Eight holes are inside a face centered cube. Eight holes are inside a face centered cube. Octahedral Hole (4 holes) One hole in the middle and 12 holes along the edges ( contributing 1/4) of the face centered cube One hole in the middle and 12 holes along the edges ( contributing 1/4) of the face centered cube

Chapter-3-19 Chemistry 481, Spring 2015 Holes in SC Unit Cells Cubic Hole

Chapter-3-20 Chemistry 481, Spring 2015 Octahedral Hole in FCC Octahedral Hole

Chapter-3-21 Chemistry 481, Spring 2015 Tetrahedral Hole in FCC Tetrahedral Hole

Chapter-3-22 Chemistry 481, Spring 2015 Structure of Metals Crystal Lattices A crystal is a repeating array made out of metals. In describing this structure we must distinguish between the pattern of repetition (the lattice type) and what is repeated (the unit cell) described above.

Chapter-3-23 Chemistry 481, Spring 2015 Polymorphism Metals are capable of existing in more than one form at a time Polymorphism is the property or ability of a metal to exist in two or more crystalline forms depending upon temperature and composition. Most metals and metal alloys exhibit this property. Uranium is a good example of a metal that exhibits polymorphism.

Chapter-3-24 Chemistry 481, Spring 2015 Alloys Substitutional Second metal replaces the metal atoms in the lattice Second metal replaces the metal atoms in the latticeInterstitial Second metal occupies interstitial space (holes) in the lattice Second metal occupies interstitial space (holes) in the lattice

Chapter-3-25 Chemistry 481, Spring 2015 Properties of Alloys Alloying substances are usually metals or metalloids. The properties of an alloy differ from the properties of the pure metals or metalloids that make up the alloy and this difference is what creates the usefulness of alloys. By combining metals and metalloids, manufacturers can develop alloys that have the particular properties required for a given use.

Chapter-3-26 Chemistry 481, Spring 2015 Structure of Ionic Solids Crystal Lattices A crystal is a repeating array made out of ions. In describing this structure we must distinguish between the pattern of repetition (the lattice type) and what is repeated (the unit cell) described above. Cations fit into the holes in the anionic lattice since anions are lager than cations. Cations fit into the holes in the anionic lattice since anions are lager than cations. In cases where cations are bigger than anions lattice is considered to be made up of cationic lattice with smaller anions filling the holes In cases where cations are bigger than anions lattice is considered to be made up of cationic lattice with smaller anions filling the holes

Chapter-3-27 Chemistry 481, Spring 2015 Basic Ionic Crystal Unit Cells

Chapter-3-28 Chemistry 481, Spring 2015 Radius Ratio Rules r+/r- Coordination Holes in Which Ratio Number Positive Ions Pack tetrahedral holes FCC octahedral holes FCC cubic holes BCC cubic holes BCC

Chapter-3-29 Chemistry 481, Spring 2015 Cesium Chloride Structure (CsCl)

Chapter-3-30 Chemistry 481, Spring 2015 Rock Salt (NaCl) © 1995 by the Division of Chemical Education, Inc., American Chemical Society. Reproduced with permission from Soli-State Resources.

Chapter-3-31 Chemistry 481, Spring 2015 Sodium Chloride Lattice (NaCl)

Chapter-3-32 Chemistry 481, Spring 2015 NaCl Lattice Calculations

Chapter-3-33 Chemistry 481, Spring 2015 CaF 2

Chapter-3-34 Chemistry 481, Spring 2015 Calcium Fluoride © 1995 by the Division of Chemical Education, Inc., American Chemical Society. Reproduced with permission from Solid-State Resources.

Chapter-3-35 Chemistry 481, Spring 2015 Zinc Blende Structure (ZnS)

Chapter-3-36 Chemistry 481, Spring 2015 Lead Sulfide © 1995 by the Division of Chemical Education, Inc., American Chemical Society. Reproduced with permission from Solid-State Resources.

Chapter-3-37 Chemistry 481, Spring 2015 Wurtzite Structure (ZnS)

Chapter-3-38 Chemistry 481, Spring 2015 Packing Efficiency

Chapter-3-39 Chemistry 481, Spring 2015 Packing Efficiency

Chapter-3-40 Chemistry 481, Spring 2015 Summary of Unit Cells Volume of a sphere = 4/3  r 3 Volume of sphere in SC = 4/3  ( ½ ) 3 = 0.52 Volume of sphere in BCC = 4/3  ((3) ½ / 4 ) 3 = 0.34 Volume of sphere in FCC = 4/3  ( 1/(2(2) ½ ) ) 3 = 0.185

Chapter-3-41 Chemistry 481, Spring 2015 Density Calculations Aluminum has a ccp (fcc) arrangement of atoms. The radius of Al = 1.423Å ( = 143.2pm). Calculate the lattice parameter of the unit cell and the density of solid Al (atomic weight = 26.98). Solution: 4 atoms/cell [8 at corners (each 1/8), 6 in faces (each 1/2)] Lattice parameter: a/r(Al) = 2(2) 1/2 a = 2(2) 1/2 (1.432Å) = 4.050Å= x cm Density = g/cm 3 Density = g/cm 3

Chapter-3-42 Chemistry 481, Spring 2015 Lattice Energy The Lattice energy, U, is the amount of energy required to separate a mole of the solid (s) into a gas (g) of its ions.

Chapter-3-43 Chemistry 481, Spring 2015 Lattice energy The higher the lattice energy, the stronger the attraction between ions. Lattice energy Compound kJ/mol LiCl834 NaCl769 KCl701 NaBr732 Na2O 2481 Na2S 2192 MgCl MgO 3795 Lattice energy Compound kJ/mol LiCl834 NaCl769 KCl701 NaBr732 Na2O 2481 Na2S 2192 MgCl MgO 3795

Chapter-3-44 Chemistry 481, Spring 2015 Lattice Energy

Chapter-3-45 Chemistry 481, Spring 2015 Properties of Ionic Compounds Crystals of Ionic Compounds are hard and brittle Have high melting points When heated to molten state they conduct electricity When dissolved in water conducts electricity

Chapter-3-46 Chemistry 481, Spring 2015 Trends in Melting Points Compound Lattice Energy (kcal/mol) (kcal/mol) NaF -201 NaF -201 NaCl -182 NaCl -182 NaBr -173 NaBr -173 NaI -159 NaI -159

Chapter-3-47 Chemistry 481, Spring 2015 Trends in Melting Points Compound Lattice Energy (kcal/mol) (kcal/mol) NaF -201 NaF -201 NaCl -182 NaCl -182 NaBr -173 NaBr -173 NaI -159 NaI -159

Chapter-3-48 Chemistry 481, Spring 2015 Compound q+ radius q- radius M.P ( o C) L.E. (kJ/mol) LiCl LiCl NaCl NaCl KCl KCl LiF LiF NaF NaF KF KF MgCl MgCl CaCl CaCl MgO MgO CaO CaO Trends in PropertiesTrends in Properties

Chapter-3-49 Chemistry 481, Spring 2015 Coulomb’s Law Coulomb’s Law k = constant q+ = cation charge q- = anion charge r = distance between two ions

Chapter-3-50 Chemistry 481, Spring 2015 Coulomb’s Model where e = charge on an electron = x C e 0 = permittivity of vacuum = x C 2 J -1 m -1 Z A = charge on ion A Z B = charge on ion B d = separation of ion centers

Chapter-3-51 Chemistry 481, Spring 2015 An ionic bond is simply the electrostatic attraction between opposite charges. Ions with charges Q1 and Q2: The potential energy is given by: d   d QQ E 21  Ionic BondsIonic Bonds

Chapter-3-52 Chemistry 481, Spring 2015 Arrange with increasing lattice energy: KCl NaF MgO KBr NaCl 788 kJ 671 kJ 3795 kJ 910 kJ 701 kJ d   K+K+ Cl    K+K+ Br  d d QQ E 21  Estimating Lattice Energy

Chapter-3-53 Chemistry 481, Spring 2015 Madelung Constant Madelung constant is geometric factor that depends on the lattice structure.

Chapter-3-54 Chemistry 481, Spring 2015 Madelung Constant Calculation

Chapter-3-55 Chemistry 481, Spring 2015 Degree of Covalent Character Fajan's Rules (Polarization)Polarization will be increased by: 1. High charge and small size of the cation 2. High charge and large size of the anion 3. An incomplete valence shell electron configuration

Chapter-3-56 Chemistry 481, Spring 2015 Trends in Melting Points Silver Halides Compound M.P. o C Compound M.P. o C AgF 435 AgF 435 AgCl 455 AgCl 455 AgBr 430 AgBr 430 AgI 553 AgI 553

Chapter-3-57 Chemistry 481, Spring 2015 Born-Lande Model: This modes include repulsions due to overlap of electron electron clouds of ions.  o = permitivity of free space A = Madelung Constant A = Madelung Constant r o = sum of the ionic radii r o = sum of the ionic radii n = average born exponet depend on the electron configuration

Chapter-3-58 Chemistry 481, Spring 2015 Born_Haber Cycle Energy Considerations in Ionic Structures

Chapter-3-59 Chemistry 481, Spring 2015 Born-Haber Cycle? Relates lattice energy ( L.E) to: Sublimation (vaporization) energy (S.E) Ionization energy metal (I.E) Bond Dissociation of nonmetal (B.E)  H f formation of NaCl(s)  H f formation of NaCl(s) L.E. = E.A.+ 1/2 B.E. + I.E. + S.E. -  H f

Chapter-3-60 Chemistry 481, Spring 2015 Ionic bond formationIonic bond formation

Chapter-3-61 Chemistry 481, Spring 2015 Energy and ionic bond formation Example - formation of sodium chloride. Steps  H o, kJ Vaporization ofNa (s) Na (g) +92 sodium Decomposition of1/2 Cl 2 (g) Cl (g) +121 chlorine molecules Ionization of sodiumNa (g) Na + (g) +496 Addition of electronCl (g) + e - Cl - (g) -349 to chlorine ( electron affinity) ( electron affinity) Formation of NaClNa + (g) +Cl - (g) NaCl -771

Chapter-3-62 Chemistry 481, Spring 2015 Energy and ionic bond formation Na (s) + 1/2 Cl2 (g) Na (g) + 1/2 Cl2 (g) Na (g) + Cl (g) Na + (s) + Cl (g) Na + (s) + Cl - (g) NaCl (s) +496 kJ(I.E.) +121 kJ(1/2 B.D.E.) +92 kJ(S.E.) -349 kJ (E.A.) -771 kJ (L.E.) -411 kJ(  Hf)

Chapter-3-63 Chemistry 481, Spring 2015 Calculation of  H f from lattice Energy

Chapter-3-64 Chemistry 481, Spring 2015 Hydration of Cations

Chapter-3-65 Chemistry 481, Spring 2015 Solubility: Lattice Energy and Hydration Energy Solubility depends on the difference between lattice energy and hydration energy holds ions and water. For dissolution to occur the lattice energy must be overcome by hydration energy.

Chapter-3-66 Chemistry 481, Spring 2015 Solubility: Lattice Energy and Hydration Energy For strong electrolytes lattice energy increases with increase in ionic charge and decrease in ionic size H hydration energies are greatest for small, highly charged ions Difficult to predict solubility from size and charge of ions. we use solubility rules.

Chapter-3-67 Chemistry 481, Spring 2015 Thermodynamics of the Solution Process of Ionic Compounds Heat of solution,  H solution : Enthalpy of hydration,  H hyd, Lattice Energy, U latt

Chapter-3-68 Chemistry 481, Spring 2015 Solution Process of Ionic CompoundsSolution Process of Ionic Compounds

Chapter-3-69 Chemistry 481, Spring 2015 Enthalpy from dipole – dipole Interactions The last term,  H L-L, indicates the loss of enthalpy from dipole - dipole interactions between solvent molecules (L) when they become solvating ligands (L') for the ions.

Chapter-3-70 Chemistry 481, Spring 2015 Hydration Process

Chapter-3-71 Chemistry 481, Spring 2015 Different types of Interactions for Dissolution

Chapter-3-72 Chemistry 481, Spring 2015 Hydration Energy of IonsHydration Energy of Ions

Chapter-3-73 Chemistry 481, Spring 2015 Hydration Process

Chapter-3-74 Chemistry 481, Spring 2015 Calculation of  H solution

Chapter-3-75 Chemistry 481, Spring 2015 Heat of Solution and Solubility

Chapter-3-76 Chemistry 481, Spring 2015 Metallic Bonding Models The difference in chemical properties between metals and non-metals lie mainly in the fact those atoms of metals fewer valence electrons and they are shared among all the atoms in the substance: metallic bonding.

Chapter-3-77 Chemistry 481, Spring 2015 Metallic solids Repeating units are made up of metal atoms, Valence electrons are free to jump from one atom to another

Chapter-3-78 Chemistry 481, Spring 2015 Electron-sea model of bonding The metallic bond consists of a series of metals atoms that have all donated their valence electrons to an electron cloud, referred to as an electron sea which permeates the entire solid. It is like a box (solid) of marbles (positively charged metal cores: known as Kernels) that are surrounded by water (valence electrons).

Chapter-3-79 Chemistry 481, Spring 2015 Electron-sea model Explanation Metallic bond together is the attraction between the positive kernels and the delocalized negative electron cloud. Fluid electrons that can carry a charge and kinetic energy flow easily through the solid making metals good electrical and thermal conductor. The kernels can be pushed anywhere within the solid and the electrons will follow them, giving metals flexibility: malleability and ductility.

Chapter-3-80 Chemistry 481, Spring 2015 Delocalized Metallic Bonding Metals are held together by delocalized bonds formed from the atomic orbitals of all the atoms in the lattice. The idea that the molecular orbitals of the band of energy levels are spread or delocalized over the atoms of the piece of metal accounts for bonding in metallic solids.

Chapter-3-81 Chemistry 481, Spring 2015 Molecular orbital theory Molecular Orbital Theory applied to metallic bonding is known as Band Theory. Band theory uses the LCAO of all valence atomic orbitals of metals in the solid to form bands of s, p, d, f bands (molecular orbitals) just like simple molecular orbital theory is applied to a diatomic molecule, hydrogen(H 2 ).

Chapter-3-82 Chemistry 481, Spring 2015 Types of conducting materials a) Conductor (which is usually a metal) is a solid with a partially full band. b) Insulator is a solid with a full band and a large band gap. c) Semiconductor is a solid with a full band and a small band gap.

Chapter-3-83 Chemistry 481, Spring 2015 Linear Combination of Atomic Orbitals

Chapter-3-84 Chemistry 481, Spring 2015 Linear Combination of Atomic Orbitals

Chapter-3-85 Chemistry 481, Spring 2015 Conduction Bands in Metals

Chapter-3-86 Chemistry 481, Spring 2015 Types of Materials A conductor (which is usually a metal) is a solid with a partially full band An insulator is a solid with a full band and a large band gap A semiconductor is a solid with a full band and a small band gap Element Band Gap C 5.47 eV Si 1.12 eV Ge 0.66 eV Sn 0 eV

Chapter-3-87 Chemistry 481, Spring 2015 Band Gaps

Chapter-3-88 Chemistry 481, Spring 2015 Band Theory of Metals

Chapter-3-89 Chemistry 481, Spring 2015 Band Theory Insulators – valence electrons are tightly bound to (or shared with) the individual atoms – strongest ionic (partially covalent) bonding. Semiconductors - mostly covalent bonding somewhat weaker bonding. Metals – valence electrons form an “electron gas” that are not bound to any particular ion

Chapter-3-90 Chemistry 481, Spring 2015 Bonding Models for Metals Band Theory of Bonding in Solids Bonding in solids such as metals, insulators and semiconductors may be understood most effectively by an expansion of simple MO theory to assemblages of scores of atoms

Chapter-3-91 Chemistry 481, Spring 2015 Band GapsBand Gaps

Chapter-3-92 Chemistry 481, Spring 2015 Doping Semiconductors